The police statement did not say if anyone was injured. Austin-Travis County emergency services posted on X that it assisted four patients, but provided no details.
Target corporate has not responded to an email from The Associated Press seeking comment.
Video shows a massive police and emergency response to the store parking lot.
Austin police identified a suspect as a white male wearing shorts and a Hawaiian-style floral shirt.
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Associated Press writers Jim Vertuno in Austin and Heather Hollingsworth in Kansas City, Missouri, contributed.